As of today, orthogonal frequency division multiplexing (OFDM) has enjoyed its dominance as the most popular signaling method in broadband wired and wireless channels. Signal modulation using OFDM has been adopted in the broad class of digital subscriber line (DSL) standards, as well as in a majority of wireless standards, such as variations of IEEE 802.11 and IEEE 802.16, the third generation partnership program long-term evolution (3GPP-LTE), and LTE-Advanced. OFDM may be used in point-to-point and downlink communications because of its low complexity and high bandwidth efficiency. The low complexity of OFDM may be a consequence of the fact that each OFDM symbol is synthesized as a summation of a number of complex-valued sinusoidal signals (e.g., “pure tones”) that are modulated by a set of quadrature amplitude modulated (QAM) data symbols. Moreover, channel distortion may be handled by adding a cyclic prefix (CP) to each OFDM symbol.
It has been noted that OFDM faces many challenges when adopted for use in more complex networks. For example, the use of OFDM during uplink of multi-user networks (e.g., orthogonal frequency division multiple access (OFDMA) networks) may require full synchronization of the users' signals at the base station input. Such synchronization has been found to be difficult to establish, particularly in mobile environments where Doppler shifts of different users are hard to predict and/or track. To address the problem of carrier and timing synchronization in OFDMA networks, resource intensive closed-loop procedures have been included to achieve the tight synchronization requirements for LTE and LTE-Advanced.
Some researchers have proposed replacing OFDM by filter bank multicarrier (FBMC) signaling. Although FBMC may overcome some of the problems of OFDM when multiple users in a network are asynchronous, application of FBMC to multiple-input and multiple-output (MIMO) channels may not be as straightforward as when OFDM is used. Other systems may include an alternative class of FBMC waveforms in which the linear convolutions used for subcarrier filtering is replaced by circular convolutions. Generalized frequency division multiplexing (GFDM) and circular FBMC (C-FBMC) are two examples of members of this class of waveforms. GFDM waveforms may be non-orthogonal and, thus, may result in a more complex receiver than C-FBMC.